In this article, I will help students to understand how to get the dimension of Pressure, Power, Force, Density, And Energy. Kindly note that before we proceed, we must first know the dimension of the fundamental quantities that we have.

In Physics, dimensional analysis is the study of the relation between physical quantities based on their units and dimensions. It is used to convert a unit from one form to another. Also, it will be easy to know the S.I base unit of any quantity in physics.

Any quantity which can be measured in units of lengths is said to have dimension, of length (L). So also any quantity which can be measured in units of time is said to have a dimension of Time (T) and any quantity which can be measured in unit of mass is said to have a dimension of Mass (Mass).

In physics, the word dimension has a special meaning. It usually denotes the physical nature of quantity. The symbol that are used to specify length, mass, and time are [L], [M], [T], respectively. They are usually enclosed in bracket.

Physical Quantity | Dimension |

Length | [L] |

Mass | [M] |

Time | [T] |

For example, the dimension of volume is [L^{3 }]. Volume is length x length x length = L X L X L = L^{3}

**Dimension for Pressure**

Pressure is defined as force per area. This can be represented mathematically as P = F/A

Force = Mass X acceleration = Mass x Velocity/Time = Mass x distance/T^{2} = M x L X T^{-2} = [MLT^{-2}]

Area = Length x Length =[ L^{2}]

Therefore, the dimension of pressure is = [MLT^{-2}]/ L^{2} = [ ML^{-1}T^{-2}]

**Dimension of Power**

Power is defined as rate of energy expended. This can be represented mathematically as Power = Force x Velocity

Force = Mass X acceleration = Mass x Velocity/Time = Mass x distance/T^{2} = M x L X T^{-2} = [MLT^{-2}]

Velocity = displacement/ Time = L/T = [ LT^{-1}]

Therefore, the dimension of power is [MLT^{-2}] /[ LT^{-1}] = [ML^{2}T^{-3}]

**Dimension of Force**

Force is product of mass and acceleration. Force = Mass X acceleration = Mass x Velocity/Time = Mass x distance/T^{2} = M x L X T^{-2} = [MLT^{-2}]

Therefore, the dimension of force is [MLT^{-2}]

**Dimension of Density**

Density is mass divided by volume i.e. Mass/Volume = M/L^{3} = ML^{-3}

The dimension of density = [ML^{-3} ]

**Dimension of Energy**

Energy is the ability to do work. Mathematically, energy = Force x distance

Force = [MLT^{-2}]

Distance = [L]

Dimension of energy = [MLT^{-2}] / [L] = [MT^{-2}]